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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

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Abstract definition of convex set

I'd like to formulate an abstract definition of convex sets: a set $K$ is convex if it is endowed with a ternary operation $K\times[0,1]\times K\to K$, written $(x:t:y)$, satisfying axioms $(x:0:y)= …
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